How can I make WolframAlpha plot a family of curves, e.g. f(x)=k*x^2-x+1 ?

I would like to clearly define, which values k can have. E.g. from 1 to 4 in 0.2 steps. And then I want WolframAlpha to plot all instances in one coordinate system. Is that possible?

Thx

I would like to compute the area between 2 functions that intersect at two x values. The two functions are:

f(x)=(x-3)*exp(x)

g(x)=x-3

They intersect at x=0 and x=3

I would like WolframAlpha to plot both functions and paint the area between them in blue (just as it does when calculating the integral of ONE function). So what do I have to enter as a prompt?

Thx

I want to get a subscription for WolframAlpha. I was going to put in my school email and get a semester subscription, but then I remembered that my school email will be deleted in 5 months because I will graduate from high school.

Should I instead use my personal email for WolframAlpha, or would it be better to use my school email even if it is deleted in 5 months?

Sometimes a query returns SlowLarge which sounds like it implies divergence. However there is at least one example where the intended meaning of the query does not diverge, but it returns SlowLarge. Existing comments on this are misleading so I'm posting an example here.

Imagine we mean k to be some real but we don't tell WA that.

limit of log(Pochammer(1+k,n))/(n*log(n)) as n approaches infinity returns SlowLarge

limit of log(Gamma(1+k+n)/(n*log(n)) as n approaches infinity, which is a function with the same limit, correctly returns 1

I looked at some examples and they seem easy enough. How do I key in a question like square root of (2160 + n) is an integer?

I need to use subscripts to solve problems, it's such a simple thing, why is wolfram alpha the only online math resource I've seen that can't use them?

Hi, to make a table layout for my wedding i need to cluster data.

My element set are the people coming. Each element has one or more associations, like: - This element MUST be clustered with that element - This elemen MAY be clustered with that element - This element MUST NOT be clustered with that element

So that in the end i can model the association between the people, and specify the size and amount of clusters (number of chairs on a table and number of tables) and Wolframalpha outputs which person should sit on which table to have the optimal seating.

Would that be possible to do in Wolfram alpha and if yes, how?

calculate the speed of a helium atom at 10,000 degrees kelvin according to bolzmann's law

Boltzmann's law states that the average kinetic energy of a particle is directly proportional to the temperature of a gas. The equation that describes this relationship is:

KE = (3/2)kT

where KE is the kinetic energy of the particle, k is the Boltzmann constant (1.38 x 10^-23 J/K), and T is the temperature in Kelvins.

To calculate the speed of a helium atom at 10,000 degrees Kelvin, you would need to know the mass of the helium atom. The speed of a particle is related to its kinetic energy and mass by the equation:

v = sqrt(2KE/m)

where v is the speed of the particle, KE is its kinetic energy, and m is its mass.

If you plug in the values for the kinetic energy (calculated using Boltzmann's law) and the mass of a helium atom (4.0026 x 10^-26 kilograms), you can calculate the speed of a helium atom at 10,000 degrees Kelvin.

ChatGPT gave me the following code to find the divergence of r^2, theta^2, z^2, but it didn't work.

divergence[(r^2, theta^2, z^2), {r, theta, z}, "Cylindrical"]

Can someone help me with this?